How flexible is the disulfide linker? A combined rotational-computational investigation of diallyl disulfide.

The symmetrically substituted diallyl disulfide adopts a non-symmetric conformation in the gas-phase, as observed with supersonic-jet rotational spectroscopy. The determination of the equilibrium structure with a predicate mixed regression illustrates both the benefits of the mass-dependent method for moderately large molecules and the structural peculiarities of the disulfide bridge.

The S-S Bridge: A Mixed Experimental-Computational Estimation of the Equilibrium Structure of Diphenyl Disulfide.

The disulfide bridge (-S-S-) is an important structural motif in organic and protein chemistry, but only a few accurate equilibrium structures are documented. We report the results of supersonic-jet microwave spectroscopy experiments on the rotational spectra of diphenyl disulfide, C6 H5 -S-S-C6 H5 (including all 13 C and 34 S monosubstituted isotopologues), and the determination of the equilibrium structure by the mixed estimation (ME) method. A single conformation of C2 symmetry was observed in the gas phase. This disulfide is a challenging target since its structure is determined by 34 independent parameters. Additionally, ab initio calculations revealed the presence of three low-frequency vibrations (<50 cm-1 ) associated to phenyl torsions which would prevent the calculation of an accurate force field. For this reason, instead of the semiexperimental method, we used the mass-dependent (rm ) method to fit the structural parameters concurrently to moments of inertia and predicate parameters, affected with appropriate uncertainties. The predicates were obtained by high-level quantum-chemical computations. A careful analysis of the results of different fits and a comparison with the ab initio optimizations confirms the validity of the used methods, providing detailed structural information on the title compound and the disulfide bridge.

Semiexperimental and mass-dependent structures by the mixed regression method: Accurate equilibrium structure and failure of the Kraitchman method for ethynylcyclohexane.

The mixed regression method for determination of molecular structures is reviewed and applied to the investigation of ethynylcyclohexane, using both semiexperimental and mass-dependent methods. This methodology provides an efficient and computationally affordable route to obtain accurate molecular reference data, preventing ill-conditioning in the structural least-squares determinations from experimental rotational constants. New supersonic-jet microwave measurements are reported to obtain inertial data for the axial and equatorial species of ethynylcyclohexane, together with all 13C isotopologues of the equatorial form. The semiexperimental equilibrium (reSE) and mass-dependent (rm(2)) structures of the molecule are compared with high-level ab initio optimizations, showing that both methods deliver compatible structures with accuracies of about 0.002 Å for bond lengths and 0.2° for bond angles. We confirm that dependable predicates can be obtained for a large variety of bonds. Finally, we verify that the substitution method completely fails to determine a reliable structure for the title compound.

Axial-equatorial isomerism and semiexperimental equilibrium structures of fluorocyclohexane.

An experimental-computational methodology combining rotational data, high-level ab initio calculations and predicate least-squares fitting is applied to the axial-equatorial isomerism and semiexperimental equilibrium structure determination of fluorocyclohexane. New supersonic-jet microwave measurements of the rotational spectra of the two molecular conformations, together with all 13C isotopologues of both isomeric forms are reported. Equilibrium rotational constants are obtained from the ground-state rotational constants corrected for vibration-rotation interactions and electronic contributions. Equilibrium structures were determined by the mixed estimation (ME) method. Different computational methods were tested for the evaluation of predicate values of the structural parameters, and a computationally effective procedure for estimating reliable dihedral angles is proposed. Structural parameters were fitted concurrently to predicate parameters and moments of inertia, affected with appropriate uncertainties. The new structures of the title compound are regarded as accurate to 0.001 Å and 0.2°, illustrating the advantages of this methodology. Structural comparisons are offered with the cyclohexane prototype, revealing subtle substituent effects. For comparison purposes the equilibrium structures for the two fluorocyclohexane isomers and cyclohexanone are computed from high-level ab initio theory with inclusion of adjustments for basis set dependence and correlation of the core electrons.

Fourier Transform Microwave Spectrum of Propene-3-d1 (CH2═CHCH2D), Quadrupole Coupling Constants of Deuterium, and a Semiexperimental Equilibrium Structure of Propene.

The ground-state rotational spectrum of propene-3-d1, CH2═CHCH2D, was measured by Fourier transform microwave spectroscopy. Transitions were assigned for the two conformers, one with the D atom in the symmetry plane (S) and the other with the D atom out of the plane (A). The energy difference between the two conformers was calculated to be 6.5 cm-1, the S conformer having lower energy. The quadrupole hyperfine structure due to deuterium was resolved and analyzed for both conformers. The experimental quadrupole coupling and the centrifugal distortion constants compared favorably to their ab initio counterparts. Ground-state rotational constants for the S conformer are 40582.157(9), 9067.024(1), and 7766.0165(12) MHz. Ground-state rotational constants for the A conformer are 43403.75(3), 8658.961(2), and 7718.247(2) MHz. For the A conformer, a small tunneling splitting (19 MHz) due to internal rotation was observed and analyzed. Using the new rotational constants of this work as well as those previously determined for the 13C species and for some deuterium-substituted species from the literature, a new semiexperimental equilibrium structure was determined and its high accuracy was confirmed. The difficulty in obtaining accurate coordinates for the out-of-plane hydrogen atom is discussed.

The equilibrium molecular structures of 2-deoxyribose and fructose by the semiexperimental mixed estimation method and coupled-cluster computations.

Fructose and deoxyribose (24 and 19 atoms, respectively) are too large for determining accurate equilibrium structures, either by high-level ab initio methods or by experiments alone. We show in this work that the semiexperimental (SE) mixed estimation (ME) method offers a valuable alternative for equilibrium structure determinations in moderate-sized molecules such as these monosaccharides or other biochemical building blocks. The SE/ME method proceeds by fitting experimental rotational data for a number of isotopologues, which have been corrected with theoretical vibration-rotation interaction parameters (αi), and predicate observations for the structure. The derived SE constants are later supplemented by carefully chosen structural parameters from medium level ab initio calculations, including those for hydrogen atoms. The combined data are then used in a weighted least-squares fit to determine an equilibrium structure (r). We applied the ME method here to fructose and 2-deoxyribose and checked the accuracy of the calculations for 2-deoxyribose against the high level ab initio r structure fully optimized at the CCSD(T) level. We show that the ME method allows determining a complete and reliable equilibrium structure for relatively large molecules, even when experimental rotational information includes a limited number of isotopologues. With a moderate computational cost the ME method could be applied to larger molecules, thereby improving the structural evidence for subtle orbital interactions such as the anomeric effect.

Interplay of experiment and theory: high resolution infrared spectrum and accurate equilibrium structure of BF2OH.

The high-resolution Fourier transform infrared (FTIR) spectrum of (11)BF2OH (difluoroboric acid) is analyzed taking into account numerous interactions. The ν1, ν2 and ν3 infrared bands are analyzed for the first time, whereas the parameters of the 6(1), 7(1), 8(1) and 9(1) states and for the 4(1) and 9(2) interacting states are redetermined. These results are used to check the quality of the ab initio force field. It is found that the ab initio rovibrational corrections are more accurate than the experimental ones. An earlier attempt to determine a semiexperimental structure did not allow us to obtain an accurate equilibrium structure. The reasons of this failure are investigated. This failure was mainly due to the lack of useful experimental information. Indeed, there is no isotopic substitution available for the fluorine atoms, and the boron atom is extremely close to the center of mass. Furthermore, the available isotopic substitutions (H → D and (16)O → (18)O) induce a large rotation of the principal axis system which amplifies the errors. However, the mixed estimation method has allowed us to determine a complete and reliable equilibrium structure. Thanks to this method, it is possible to determine an accurate structure, even in extremely difficult cases. An extensive analysis of the quality of structure calculations at the CCSD(T) level is also performed using basis sets up to five ζ quality. It was found that, at the convergence limit, the effects of the diffuse functions are practically disappearing, whereas the core-core and core-valence electron correlation effects are quite important for the bond lengths.

Electron delocalization in polyenes: a semiexperimental equilibrium structure for (3E)-1,3,5-hexatriene and theoretical structures for (3Z,5Z)-, (3E,5E)-, and (3E,5Z)-1,3,5,7-octatetraene.

Electronic structure theory reveals that π-electron delocalization increases with the chain length in polyenes. To analyze quantitatively this effect a semiexperimental equilibrium structure has been determined for trans-hexatriene by the mixed estimation method. For this fit rotational constants for a number of carbon and hydrogen isotopologues as well as a high-level ab initio structure have been used. The accuracy is 0.001 Å for bond lengths and 0.1° for bond angles. For the three isomers of octatetraene, high-level ab initio calculations have given a comparably accurate structure. These structures have been used in comparison with the structure of s-trans-butadiene to show that "C═C" bonds increase in length and "C-C" bonds decrease in length as the polyene chain lengthens. These structural effects of π-electron delocalization increase toward the center of polyenes. Most likely, π-π conjugation in the molecules studied plays a large part in their planarity that, in turn, forces the hydrogen atoms of cis fragments in bay regions to be in a close contact. Their distance is indeed shorter than the sum of their van der Waals radii, and they seem to participate in a six-membered ring.

Equilibrium structures of three-, four-, five-, six-, and seven-membered unsaturated N-containing heterocycles.

Up to six different techniques are utilized to estimate the equilibrium structures (r(e)) of a series of mostly unsaturated, N-containing heterocycles. Accurate Born-Oppenheimer (r(e)(BO)) and, if allowed, semiexperimental (r(e)(SE)), as well as empirical (r(m)-type) estimates of the equilibrium structures of three-membered (1H- and 2H-azirine, aziridine), four-membered (azete), five-membered (pyrrole, pyrazole, imidazole), six-membered (pyridine, pyrimidine, uracil), and seven-membered (1H-azepine) rings, containing usually one but in some cases two N atoms, are determined. The agreement among the structural results of the different techniques is very satisfactory. It is shown that it is possible to use the CCSD(T) electronic structure method with the relatively small wCVTZ basis set, with all electrons correlated, and the effect of further basis set enlargement, wCVTZ → wCVQZ, computed at the MP2 level, to obtain reliable equilibrium structures for the semirigid molecules investigated. Extension to larger basis sets does not significantly improve the accuracy of the computed results. Although all molecules investigated are oblate, and their principal axis system is subject to large rotations upon isotopic substitution, the semiexperimental method, when applicable, provides accurate results, though in the difficult cases it must be augmented with the mixed regression method. Finally, it is noteworthy that the empirical mass-dependent (r(m)) method also delivers surprisingly accurate structures for this class of compounds.

Accurate equilibrium structures for piperidine and cyclohexane.

Extended and improved microwave (MW) measurements are reported for the isotopologues of piperidine. New ground state (GS) rotational constants are fitted to MW transitions with quartic centrifugal distortion constants taken from ab initio calculations. Predicate values for the geometric parameters of piperidine and cyclohexane are found from a high level of ab initio theory including adjustments for basis set dependence and for correlation of the core electrons. Equilibrium rotational constants are obtained from GS rotational constants corrected for vibration-rotation interactions and electronic contributions. Equilibrium structures for piperidine and cyclohexane are fitted by the mixed estimation method. In this method, structural parameters are fitted concurrently to predicate parameters (with appropriate uncertainties) and moments of inertia (with uncertainties). The new structures are regarded as being accurate to 0.001 Å and 0.2°. Comparisons are made between bond parameters in equatorial piperidine and cyclohexane. Another interesting result of this study is that a structure determination is an effective way to check the accuracy of the ground state experimental rotational constants.

Why it is sometimes difficult to determine the accurate position of a hydrogen atom by the semiexperimental method: structure of molecules containing the OH or the CH3 group.

The semiexperimental (SE) technique, whereby equilibrium rotational constants are derived from experimental ground-state rotational constants and corrections based on an ab initio cubic force field, has the reputation to be one of the most accurate methods to determine an equilibrium structure ( reSE). However, in some cases, it cannot determine accurately the position of the hydrogen. To investigate the origins of this difficulty, the SE structures of several molecules containing either the OH or the CH3 group are determined and compared to their best ab initio counterparts. It appears that an important factor is the accuracy of the geometry used to calculate the force field, in particular when the least-squares system is not well conditioned. In this case, the mixed regression method is often an easy way to circumvent this difficulty.

Semiexperimental equilibrium structures for cis,cis- and trans,trans-1,4-difluorobutadiene by the mixed estimation method and definitive relative energies of the isomers.

Equilibrium molecular structures accurate to 0.001 Å and 0.2° have been determined for cis,cis- and trans,trans-1,4-difluorobutadiene by the semiexperimental mixed estimation method. In this method, structures are fitted concurrently to equilibrium rotational constants and bond parameters obtained from an intermediate level of electronic structure theory. The effect of fluorine substitution on the carbon backbone of butadiene is surprisingly small. Definitive energy differences for the ground states were computed, employing the focal-point analysis (FPA) technique, between the trans,trans and cis,cis isomers (ΔH°0 = 5.6(3) kJ mol(-1)) and the cis,trans and cis,cis isomers (ΔH°0 = 3.2(2) kJ mol(-1)) of 1,4-difluorobutadiene. These differences confirm the exceptional relationship that the trans,trans isomer has the highest energy and the cis,cis isomer the lowest energy, endorsing what was reported earlier on the basis of experimental observations in benzene solution.

Accurate determination of the deformation of the benzene ring upon substitution: equilibrium structures of benzonitrile and phenylacetylene.

Accurate equilibrium, re, structures of the monosubstituted benzene molecules benzonitrile, C6H5CN, and phenylacetylene, C6H5CCH, have been determined using two different, to some extent complementary techniques. The semiexperimental, r(e)(SE), structural parameters are the result of a least-squares fit to equilibrium rotational constants derived from experimental effective ground-state rotational constants and rovibrational corrections based principally on an ab initio cubic force field. The composite ab initio Born-Oppenheimer, r(e)(BO), structural parameters are obtained from frozen-core and all-electron MP2 and the CCSD(T) geometry optimizations using Gaussian basis sets up to quintuple-zeta quality. The DFT(B3LYP) method, with two different Gaussian basis sets, 6-31G* and 6-311+G(3df,2pd), was used to calculate the cubic force field employed during the r(e)(SE) structure determination. With the 6-31G* basis set, the error of the rovibrational correction is to a large extent random, whereas with the 6-311+G(3df,2pd) basis set it is mainly systematic. As shown here, systematic errors do not have a significant effect on the accuracy of the derived structure; the quality of the structural fit, however, is sensitive to the true accuracy of the ground-state rotational constants. An even more important general conclusion of this study is that the addition of extra rotational constants from multisubstituted species does not seem to improve the accuracy of the r(e)(SE) structures, quite in contrast to the highly desirable availability of data corresponding to all singly substituted species.

Accurate semiexperimental structure of 1,3,4-oxadiazole by the mixed estimation method.

In order to determine an accurate equilibrium structure for 1,3,4-oxadiazole, microwave transitions and ground-state rotational constants are reported for the parent species and for the (18)O isotopologue measured in natural abundance. These rotational constants along with those of the (13)C, (15)N, and D1 species were used together with vibration-rotation constants calculated from a cubic force field calculated at the B3LYP/6-311+G(3df,2pd) level of theory to derive a semiexperimental equilibrium structure. However, the results of this fit were not satisfactory; therefore, the structure was later significantly improved by the mixed estimation method. In this method, internal coordinates from good-quality quantum chemical calculations (with appropriate uncertainties) are fitted simultaneously with moments of inertia of the full set of isotopologues. The accuracy of this structure has been confirmed by using an extrapolation technique. All elements of the (14)N nuclear quadrupole coupling tensor have been determined.

Microwave spectra of the deuterium isotopologues of cis-hexatriene and a semiexperimental equilibrium structure.

Microwave transitions and ground state rotational constants are reported for five newly synthesized deuterium isotopologues of cis-1,3,5-hexatriene (cHTE). These rotational constants along with those of the parent and the three (13)C species are used with vibration-rotation constants calculated from an MP2/cc-pVTZ model to derive an equilibrium structure. That structure is improved by the mixed estimation method. In this method, internal coordinates from good-quality quantum chemical calculations (with appropriate uncertainties) are fit simultaneously with moments of inertia of the full set of isotopologues. The new structure of cHTE is confirmed to be planar and is stabilized by an interaction between the hydrogen atoms H2 and H5, which form a bond and participate in a six-membered ring. cHTE shows larger structural effects of π-electron delocalization than does butadiene with the effects being magnified in the center of the molecule. Thus, strong structural evidence now exists for an increase in π-electron delocalization as the polyene chain lengthens.

Semiexperimental equilibrium structures for the equatorial conformers of N-methylpiperidone and tropinone by the mixed estimation method.

N-Methylpiperidone (MPIP) and tropinone, which contain a structural motif found in numerous alkaloids, are too large to determine an accurate equilibrium structure either by ab initio methods or by experiment. However, the ground state rotational constants of the parent species and of all isotopologues with a substituted heavy atom ((13)C, (15)N, (18)O) are known from microwave spectroscopy. These constants have been corrected for the rovibrational contribution calculated from an ab initio cubic force field. These semiexperimental equilibrium rotational constants have been supplemented by carefully chosen structural parameters from medium level ab initio calculations. The two sets of data have been used in a weighted least-squares fit to determine reliable equilibrium structures for both molecules. This work shows that it is possible to determine reliable equilibrium structures for large molecules (34 degrees of freedom in the case of tropinone) at a detailed level of accuracy, and the method could be applied without too much difficulty to still larger molecules.

Semiexperimental equilibrium structure of the lower energy conformer of glycidol by the mixed estimation method.

Rotational constants were determined for (18)O-substituted isotopologues of the lower energy conformer of glycidol, which has an intramolecular inner hydrogen bond from the hydroxyl group to the oxirane ring oxygen. Rotational constants were previously determined for the (13)C and the OD species. These rotational constants have been corrected with the rovibrational constants calculated from an ab initio cubic force field. The derived semiexperimental equilibrium rotational constants have been supplemented by carefully chosen structural parameters, including those for hydrogen atoms, from medium level ab initio calculations. The combined data have been used in a weighted least-squares fit to determine an equilibrium structure for the glycidol H-bond inner conformer. This work shows that the mixed estimation method allows us to determine a complete and reliable equilibrium structure for large molecules, even when the rotational constants of a number of isotopologues are unavailable.

Equilibrium structures of heterocyclic molecules with large principal axis rotations upon isotopic substitution.

Equilibrium structures, r(e), of the heterocyclic molecules oxirane, furazan, furan, ethylene ozonide, and 1,3,4-oxadiazole have been determined using three different, somewhat complementary techniques: a completely experimental technique (r(m)), a semiexperimental technique (r(e)(SE), whereby equilibrium rotational constants are derived from experimental effective ground-state rotational constants and corrections based principally on an ab initio cubic force field), and an ab initio technique (r(e)(BO), whereby geometry optimizations are usually performed at the coupled cluster level of theory including single and double excitations augmented by a perturbational estimate of the effects of connected triple excitations [CCSD(T)] using quadruple-ζ Gaussian basis sets). All these molecules are asymmetric tops with the moment of inertia I(c) much larger than the other two moments of inertia, I(a) and I(b). Molecules of this shape experience a large rotation of the principal axis system upon certain isotopic substitutions. For such isotopologues it is difficult to obtain a good structural fit to the semiexperimental moments of inertia I(a) and I(b), which may significantly reduce the accuracy of the r(e)(SE) structural parameters. The origin of this difficulty is explained. For the heavy-atom skeleton of these molecules it was possible to determine a rather accurate empirical mass-dependent structure without a priori knowledge of the equilibrium structure.